How to Quickly Calculate Square of Any Two Digit Number?

In this post I’ve tried to improvise on the method of squaring presented in one of the earlier posts on itself. This trick of squaring any two digit number with ease is inspired by squaring techniques from the book – The Trachtenberg Speed System of Basic Mathematics

I would like to explain this method of squaring any 2 digits number with the help of an illustration.

What is the square of 32?

Step 1. In finding the last two digits of the answer, we shall find the square of the last digit of the number. Square the right-digit digit, which is 2 in this case. Hence we get 04

_ _04

Step 2. We shall now need to use the cross product. This is what we get when we multiply the two digits of the given number together. Multiply the two digits of the number together and double it: 3 times 2 is 6, doubled is 12: We write 12 as 2 and carry over 1 to the next step.

_ 24

Step 3: In finding the first two digits of the answer we shall still need to square the first digit of the number. That means we square the left hand figure of the number. Here square of 3 will be 9. Add 1 which is carried over from last step. Hence we get 9 + 1 =10


That’s the answer.

This method can also be compared with another shortcut to find the square of any number posted by me on in the past.

Let’s try another example by squaring 64.

Square of 64 =     Square of 6 | double of cross product of both given digits 4 & 6| square of 4

Square of 64 =      36 |2x6x4 | 16

=      36 | 48 | 16

Collapsing the numbers

=      36 | 48 + 1 | 6

=      36 + 4 | 9 | 6

=      40 | 9 | 6

Hence the answer is 4096.

Have you come across any other squaring method like this?

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

12 thoughts to “How to Quickly Calculate Square of Any Two Digit Number?”

    1. Method works for all numbers. for 116 or 121 we have to go like this. let us take 116 first. it is 16 more than 100 so first part will be 116+16=132. second part will be 16^2 =256. but only two digits are to be taken for last part i.e. 56 and 3rd digit which is 2 is to use as carry to first part, which will become 134. Speak full answer like 13456.
      similarly ,for 121 the square is |121+21|441|=14641 ( 121+21=142+4 as carry from last part so first 3 digits are 146 last two digits are 41 from square of 21=441.

      1. You can also use (a+b)^2.Using this method you can split 121 as 100+21
        10000+4200+441 = 14541 OR you can split 121 as (120+1)^2. This gives:
        14400+240+1 = 14641

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